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Semilinear Schrödinger Equations

Thierry Cazenave Université de Paris VI, Pierre et Marie Curie, Paris, France
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Available Formats:
Softcover ISBN: 978-0-8218-3399-5
Product Code: CLN/10
List Price: $52.00 MAA Member Price:$46.80
AMS Member Price: $41.60 Electronic ISBN: 978-1-4704-1760-4 Product Code: CLN/10.E List Price:$49.00
MAA Member Price: $44.10 AMS Member Price:$39.20
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $62.40 Click above image for expanded view Semilinear Schrödinger Equations Thierry Cazenave Université de Paris VI, Pierre et Marie Curie, Paris, France A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University Available Formats:  Softcover ISBN: 978-0-8218-3399-5 Product Code: CLN/10  List Price:$52.00 MAA Member Price: $46.80 AMS Member Price:$41.60
 Electronic ISBN: 978-1-4704-1760-4 Product Code: CLN/10.E
 List Price: $49.00 MAA Member Price:$44.10 AMS Member Price: $39.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$62.40
• Book Details

Courant Lecture Notes
Volume: 102003; 323 pp
MSC: Primary 35;

The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or the Korteweg-de Vries equation. From the mathematical point of view, Schrödinger's equation is a delicate problem, possessing a mixture of the properties of parabolic and elliptic equations. Useful tools in studying the nonlinear Schrödinger equation are energy and Strichartz's estimates.

This book presents various mathematical aspects of the nonlinear Schrödinger equation. It studies both problems of local nature (local existence of solutions, uniqueness, regularity, smoothing effect) and problems of global nature (finite-time blowup, global existence, asymptotic behavior of solutions). In principle, the methods presented apply to a large class of dispersive semilinear equations. The first chapter recalls basic notions of functional analysis (Fourier transform, Sobolev spaces, etc.). Otherwise, the book is mostly self-contained.

It is suitable for graduate students and research mathematicians interested in nonlinear partial differential equations and applications to mathematical physics.

Graduate students and research mathematicians interested in nonlinear partial differential equations and applications to mathematical physics.

• Chapters
• Chapter 1. Preliminaries
• Chapter 2. The linear Schrödinger equation
• Chapter 3. The Cauchy problem in a general domain
• Chapter 4. The local Cauchy problem
• Chapter 5. Regularity and the smoothing effect
• Chapter 6. Global existence and finite-time blowup
• Chapter 7. Asymptotic behavior in the repulsive case
• Chapter 8. Stability of bound states in the attractive case
• Chapter 9. Further results

• Reviews

• The book, written by one of the leading expert on the subject, is also an up-to- date source of references for recent results and open problems, well represented in its extensive bibliography. It can certainly be used as a guideline for a course to an audience with a sufficient background on functional analysis and partial differential equations.

Zentralblatt MATH
• In summary, the author gives a well balanced treatment of the many types of mathematical results... This book would be an excellent place to start for readers interested in an introduction to these topics. There is an extensive bibliography which nicely complements the author's discussions.

Woodford W. Zachary for Mathematical Reviews
• Request Review Copy
Volume: 102003; 323 pp
MSC: Primary 35;

The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or the Korteweg-de Vries equation. From the mathematical point of view, Schrödinger's equation is a delicate problem, possessing a mixture of the properties of parabolic and elliptic equations. Useful tools in studying the nonlinear Schrödinger equation are energy and Strichartz's estimates.

This book presents various mathematical aspects of the nonlinear Schrödinger equation. It studies both problems of local nature (local existence of solutions, uniqueness, regularity, smoothing effect) and problems of global nature (finite-time blowup, global existence, asymptotic behavior of solutions). In principle, the methods presented apply to a large class of dispersive semilinear equations. The first chapter recalls basic notions of functional analysis (Fourier transform, Sobolev spaces, etc.). Otherwise, the book is mostly self-contained.

It is suitable for graduate students and research mathematicians interested in nonlinear partial differential equations and applications to mathematical physics.

Graduate students and research mathematicians interested in nonlinear partial differential equations and applications to mathematical physics.

• Chapters
• Chapter 1. Preliminaries
• Chapter 2. The linear Schrödinger equation
• Chapter 3. The Cauchy problem in a general domain
• Chapter 4. The local Cauchy problem
• Chapter 5. Regularity and the smoothing effect
• Chapter 6. Global existence and finite-time blowup
• Chapter 7. Asymptotic behavior in the repulsive case
• Chapter 8. Stability of bound states in the attractive case
• Chapter 9. Further results
• The book, written by one of the leading expert on the subject, is also an up-to- date source of references for recent results and open problems, well represented in its extensive bibliography. It can certainly be used as a guideline for a course to an audience with a sufficient background on functional analysis and partial differential equations.

Zentralblatt MATH
• In summary, the author gives a well balanced treatment of the many types of mathematical results... This book would be an excellent place to start for readers interested in an introduction to these topics. There is an extensive bibliography which nicely complements the author's discussions.

Woodford W. Zachary for Mathematical Reviews
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